656 
PROFESSOR CAYLEY’S TENTH MEMOIR ON QUANTICS. 
and 
( 1 
4- ft 48 )* 0 
( 
a 4 
+ ft 6 
+ ft 10 
+ 
lO 
)ft* 
( 
a 4 
+ ft 6 
+ ft 8 
+ « 10 
+ ft 44 
— ft 48 ) ft 3 * 3 
( 1 
+ft 3 
+ft 4 
+ ft 8 
)ft 3 * 3 
( 1 
+ft 3 
+a. 4 
+ ft 6 
+ ft 46 
-ft 14 
)ft 4 * 4 
( 1 
+ft 4 
-b« 6 
-ft 46 
)ft 3 * 5 
( 
a 2 
-ft 13 
-ft 14 
)ft 3 * 6 
( 
«. 4 
-a 8 
-ft 13 
-ft 44 
-ft 46 
— ft 48 ) ft* 7 
( 
-ft 10 
-ft 13 
-ft 14 
-ft 46 
— ft 48 ) a 3 * 8 
( 
-a 4 
-ft 8 
-a 10 
-ft 13 
-ft 44 
)ft 3 * 3 
( 
-a 6 
-a, 8 
-ft 43 
-ft 44 
) a 4 * 40 
(-1 
— a. 48 ) a. 5 * 44 
divided bj 
1 - a 4 . 1 - a 8 . 1 - a 13 . 1 - ax 5 . 1 - a V. 1 - ft 3 * 6 
this last being in fact equivalent to that used for the determination of the R.G.F. 
386. For the sextic the forms are, N.G.F. = 
( 1 
+ ft 
-a 3 
— a 4 
— a. 5 
+ 
+ ft 8 )*° 
(-1 
— a 
+ft 3 
+ 2ft 3 
+ 2ft 4 
+ a 5 
-ft 7 
— ft 8 ) a* 3 
(-1 
+ft 3 
+ ft 3 
+ a. 4 
+ ft 5 
-ft 7 
— ft 8 ) a* 4 
( 1 
+« 
— a 3 
— a 4 
-ft 5 
-ft 6 
+ ft 8 )ft 3 * 6 
( 1 
-a, 3 
-2ft 4 
— 2ft 5 
— a, 6 
+ ft 7 
+ ft 8 )ft 3 * 8 
(-1 
— a 
+ a 3 
+ ft 4 
+ ft 5 
-a 7 
— ft 8 ) ft 3 * 40 
divided by 
1 + ft. 1 — a 3 . 1— «, 3 . 1 — a, 4 . 1— a 5 , l — ft* 6 . 1— «.* 4 . 1 — a* 3 
